Observational Correlation Between Magnetic Field, Angular Momentum, and Fragmentation in the Envelopes of Class 0 Protostars?

Astronomy & Astrophysics manuscript no. Galametz2020b © ESO 2021 January 28, 2021

Observational correlation between magnetic field, angular momentum, and fragmentation in the envelopes of Class 0 protostars? Maud Galametz1, Anaelle¨ Maury1,2, Josep M. Girart3,4, Ramprasad Rao2, Qizhou Zhang2, Mathilde Gaudel5, Valeska Valdivia1, Patrick Hennebelle1, Victoria Cabedo-Soto1, Eric Keto2, Shih-Ping Lai6

1 Astrophysics department, CEA/DRF/IRFU/DAp, Universite´ Paris Saclay, UMR AIM, F-91191 Gif-sur-Yvette, France, e-mail: [email protected] 2 Center for Astrophysics | Harvard & Smithsonian, 60 Garden street, Cambridge, MA 02138, USA 3 Institut de Ciencies` de l’Espai (ICE, CSIC), Can Magrans, S/N, E-08193 Cerdanyola del Valles,` Catalonia, Spain 4 Institut d’Estudis Espacials de de Catalunya (IEEC), E-08034 Barcelona, Catalonia, Spain 5 LERMA, Observatoire de Paris, 61 av. de l’Observatoire F-75014 Paris, France 6 Institute of Astronomy and Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan

Preprint online version: January 28, 2021

ABSTRACT

Aims. Our main goal in this analysis is to assess the potential role of magnetic fields in regulating the envelope rotation, the formation of disks, and the fragmentation of Class 0 protostars in multiple systems. Methods. We used the Submillimeter Array to carry out observations of the dust polarized emission at 0.87 mm in the envelopes of a large sample of 20 Class 0 protostars. We estimated the mean magnetic field orientation over the central 1000 au envelope scales to characterize the orientation of the main component of the organized magnetic field at the envelope scales in these embedded protostars. This direction was compared to that of the protostellar outflow in order to study the relation of their misalignment and the kinematics of the circumstellar gas. The latter is traced through the velocity gradient that is observed in the molecular line emission + (mainly N2H ) of the gas at intermediate envelope scales. Results. We discover that the misalignment of the magnetic field orientation is strongly related to the outflow and the amount of angular momentum observed at similar scales in the protostellar envelope. This reveals a potential link between the kinetic and the magnetic energy at envelope scales. The relation could be driven by favored B-misalignments in more dynamical envelopes or by a dependence of the envelope dynamics on the initial large-scale B configuration. By comparing the trend with the presence of fragmentation, we observe that single sources are mostly associated with conditions of low angular momentum in the inner envelope and good alignment of the magnetic field with protostellar outflows at intermediate scales. Our results suggest that the properties of the magnetic field in protostellar envelopes are tightly related to the rotating infalling gas that is directly involved in the formation of stars and disks: we find that it may not only affect the fragmentation of protostellar cores into multiple stellar systems, but also sets the conditions that establish the pristine properties of planet-forming disks. Key words. Stars: formation, protostars, low-mass, circumstellar matter – ISM: magnetic fields, kinematics and dynamics – Submillimeter: ISM – Instrumentation: interferometers, polarimeters – Methods: observational

1. Introduction the efficiency of the star formation process, the global properties of stars in our Galaxy, and the setting of the conditions that allow A majority of stars in our Galaxy are found in multiple stellar disks and planets to form around them. systems, and a significant fraction of solar-type stars will host planetary systems (Ducheneˆ & Kraus 2013; Hsu et al. 2019). Magnetic fields (hereafter B) are ubiquitous in the Universe Most of the final stellar mass is collected during a short but vig- (Vallee´ 2004) and have been observed to permeate the inter- orous accretion phase. During this so-called protostellar phase, stellar material deep down into star-forming cores and proto-

arXiv:2010.12466v2 [astro-ph.GA] 27 Jan 2021 the star forms at the center of an infalling rotating core, concomi- stellar environments (Girart et al. 2006; Hull & Zhang 2019). tantly with a surrounding disk of gas in circular orbits around the From a theoretical point of view, the presence of B in star- star: while the star will inherit the majority of the accreted mass, forming cores has been shown to significantly alter the dynamics most of the angular momentum contained in the protostellar en- of the gas participating in the building of stars during the accre- velope is expected to be expelled or stored in the protostellar tion phase, and it affects the resulting properties of these stars disk. This evolution will eventually lead to protoplanetary sys- and associated circumstellar disks (Terebey et al. 1984; Wurster tems (Zhao et al. 2020). Class 0 objects are the youngest accret- & Li 2018; Hennebelle & Inutsuka 2019). The mechanism for ing protostars and are surrounded by a dense envelope that is evacuating angular momentum from the infalling gas through accreted onto the central protostellar embryo during a short (t < magnetic torques applied by Alfven´ waves is called magnetic 5×104 yr) accretion phase (Andre´ et al. 2000; Evans et al. 2009). braking. The initial global collapse, driven by gravity, drags the Characterizing the dynamics of the gas and the physical pro- field lines, which leads to an hourglass morphology of the field cesses of these youngest protostars is crucial for understanding lines and amplifies the magnetic intensity. The magnetic braking

1 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars seems to be particularly enhanced by the pinching of field lines, ported in the literature. A potential link between the envelope which lengthens the magnetic lever arms and efficiently trans- dynamics and the B orientation might be an additional signa- ports the angular momentum from the inner envelope toward ture that B has a strong effect on the collapse and fragmentation, the outer one (Galli et al. 2006). As less angular momentum is as has also been suggested by the analysis of massive cores by transported toward the forming star, only small protoplanetary Zhang et al. (2014). disks form while the star grows (Allen et al. 2003; Hennebelle We complement the Galametz et al. (2018) observations with & Fromang 2008; Masson et al. 2016; Hirano & Machida 2019). eight additional Class 0 envelopes observed with the SMA at The importance of the misalignment between magnetic field 0.87mm at comparable scales. The full SMA B measurements and rotation axis has been stressed by several authors (Ciardi are combined with gas kinematics information obtained ho- + & Hennebelle 2010; Joos et al. 2012; Gray et al. 2018). They mogeneously from N2H observations of velocity gradients in found that in ideal magnetohydrodynamic (MHD) calculations, the envelopes, either from the Continuum And Lines in Young only small disks form or even no disk forms in the aligned con- ProtoStellar Objects survey (CALYPSO; Maury et al. 2019; figurations when the field is strong enough; and it is compara- Gaudel et al. 2020, seven sources) or from observations pub- tively far easier to form a disk in the misaligned case. Numerical lished in the literature that we reprocessed when required (12 simulations taking into account non-ideal MHD effects (such sources, see Table 4). Our goal is to observationally test the the- as ambipolar diffusion or Hall effect) were able to overcome oretical predictions of the conditions required for magnetic brak- the magnetic braking catastrophe, leading to the formation of ing affecting the collapse and assess the potential role of B in disks similar to those observed (Hennebelle et al. 2016; Zhao regulating the matter infall and envelope rotation, the formation et al. 2018; Wurster & Bate 2019). Studies by Hennebelle et al. of disks, and the fragmentation into multiple systems. (2020) or Wurster & Lewis (2020) appear to also predict that the misalignment of the magnetic field with the envelope rotation axis directly affects the protostellar disk formation, for instance, leading to the formation of larger planet-forming disks in the 2. Observations misaligned cases that were investigated compared to the smaller disks that are observed in aligned cases. This is particularly clear 2.1. Sample description when the field intensity is such that the mass-to-flux ratio is on Galametz et al. (2018) presented 12 low-mass Class 0 protostars the order of 10. Another key prediction of magnetized models is observed in polarization at 345 GHz with the SMA. We comple- that a strong, organized B partly alters the ability of the envelope ment this first subsample with 8 additional low-mass protostars. to fragment. This suggests that B is one of the regulating agents The 20 sources cover a wide range of protostellar properties: iso- that drive the birth of the multiple stellar systems we commonly lated, binary, triple, or quadruple systems form in cores whose observe in the Galaxy (Hennebelle & Teyssier 2008). masses range from 0.2 to 12M . Details of the full sample are The effect of the various characteristics of the B field (ori- provided in Table 1. entation with the collapse direction and strength), however, is poorly quantified observationally speaking. Only a few studies have attempted to test the predicted relation that links the B- 2.2. SMA dust polarization observations field orientation in protostellar cores to the magnitude of the an- gular momentum of the gas responsible for disk properties and The observations (taken in both compact and sub-compact con- the formation of multiple stellar systems (see, e.g., the works figurations), data reduction and polarization maps of the first 12 of Chapman et al. 2013; Hull et al. 2013; Zhang et al. 2014). low-mass Class 0 protostars observed are presented in Galametz Because it is difficult to trace B in these small embedded as- et al. (2018). The observations of the 8 additional low-mass pro- trophysical structures, it has so far been difficult to reach the tostars were obtained with the SMA settled in compact con- statistical significance that would allow us to draw firm con- figuration in the 345 GHz band (Project 2018B-S015, PI: A. clusions about the role of magnetic braking in the formation of Maury). The antennas used for each observation date are listed stars and disks (Yen et al. 2015a; Maury et al. 2018). In order to in Table 2. The polarimeter on the SMA makes use of a quarter- statistically investigate the B-field orientation, we carried out a wave plate (QWP) in order to convert the linear polarization SubMillimeter Array (SMA) survey of 20 low-mass Class 0 pro- into circular polarization. The antennas are switched between tostars, using 0.87 mm polarized dust emission. Because asym- polarizations (QWP are rotated at various angles) in a coordi- metric dust particles of the interstellar medium align themselves nated temporal sequence to sample the various combinations with their minor axis parallel to the B-field lines (Andersson of circular polarizations on each baseline. A variety of obser- et al. 2015), the observed polarized angle provides us with a ro- vational modes (single- and dual-receiver polarization modes) bust proxy of the direction perpendicular to the magnetic field were used for the observations of Galametz et al. (2018). The orientation. Class 0 objects were ideally suited for this analysis dual-receiver full polarization mode, fully commissioned, was because most of the mass that collapses onto the central embryo then the only mode we used to observe the additional 8 tar- still resides in the envelope, allowing us to trace the B orienta- gets. The new observations were also taken using the SMA tion at envelope (1000-2000 au) scales. Galametz et al. (2018) Wideband Astronomical ROACH2 Machine (SWARM) rather presented results for a first subsample of 12 sources, focusing than the Application-Specific Integrated Circuit (ASIC) correla- on the properties of polarization fractions and general alignment tor: the added bandwidth has helped increase the SMA sensitiv- between B and the outflow at envelope scales. We reported the ity. A detailed description of the SMA polarimeter system is pro- detection of linearly polarized dust emission in all the objects vided by Marrone (2006) and Marrone & Rao (2008). Frequent of the sample. By comparing the B orientation with that of the observations of various calibrators were taken between the target outflow axis, which is commonly used as a proxy for the rota- observations to ensure the future gain and polarization calibra- tional axes of these systems, we noted that at the scales traced tion. Flux calibrators (Callisto and Neptune) were also observed, in our analysis, the B-field lines were preferentially misaligned but were not used when we performed the flux calibration of the in sources for which large equatorial velocity gradients were re- observations (see § 2.3).

2 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Table 1. Characteristics of the full sample.

Name α (J2000) δ (J2000) Cloud Distance Menv References (pc) Per B1-bSa 03:33:21.35 +31:07:26.4 Perseus / Barnard 230 3.0 [2, 12] Per B1-ca 03:33:17.88 +31:09:32.0 Perseus / Barnard 230 2.1 [2, 11] B335 19:37:00.90 +07:34:09.6 isolated 100 1.3b [3, 15] BHR7-MMSa 08:14:23.33 -34:31:03.7 Gum / Vela 400 1.0 [5, 13] CB230 21:17:40.00 +68:17:32.0 Cepheus 352 3.4 [4, 14] HH25-MMSa 05:46:07.40 -00:13:43.4 Orion / L1630 400 0.5 [6, 16] HH211-mma 03:43:56.52 +32:00:52.8 Perseus / IC348 320 1.5 [1, 16] HH212∗ 05:43:51.40 -01:02:53.0 Orion / L1630 400 0.2 [6, 17] HH797 03:43:57.10 +32:03:05.6 Perseus / IC348 320 1.1 [1, 19] IRAS03282 03:31:20.40 +30:45:24.7 Perseus 293 2.2 [1, 18] IRAS16293-A 16:32:22.9 -24:28:36.0 Ophiuchus 150 2.3 [8, 16] L1157 20:39:06.3 +68:02:15.8 Cepheus 352 3.0 [4, 10] L1448C 03:25:38.9 +30:44:05.4 Perseus 293 2.0 [1, 10] L1448N-B 03:25:36.3 +30:45:14.9 Perseus 293 4.8 [1, 10] L1448-2A 03:25:22.4 +30:45:13.0 Perseus 293 1.9 [1, 10] L483-mma 18:17:29.94 -04:39:39.3 Serpens Cirrus 250 1.8 [7, 18] NGC 1333 IRAS4A 03:29:10.5 +31:13:31.0 Perseus 293 12.3 [1, 10] NGC 1333 IRAS4B 03:29:12.0 +31:13:08.0 Perseus 293 4.7 [1, 10] Serpens South MM18a 18:30:04.12 -02:03:02.55 Serpens South 350 5 [9, 10] SVS13-B 03:29:03.1 +31:15:52:0 Perseus 293 2.8 [1, 10]

a Sources whose SMA polarization observations are described in this paper. The polarization results for the remaining sources are described in Galametz et al. (2018), Girart et al. (2014), and Rao et al. (2009). b The total globule mass is probably a factor of 3-5 higher (Stutz et al. 2008).

References for the distances and Menv - [1] Ortiz-Leon´ et al. (2018a), [2] Cernisˇ & Straizysˇ (2003), [3] Olofsson & Olofsson (2009), [4] Zucker et al. (2019), [5] Woermann et al. (2001), [6] Anthony-Twarog (1982) [7] Herczeg et al. (2019) [8] Ortiz-Leon´ et al. (2018b), [9] Ongoing work re-analyzing the Gaia data toward Serpens South suggests a high extinction layer up to distances of 350 pc (Palmeirim, Andre´ et al. in prep). We use this reevaluated distance. [10] Maret et al. (2020), [11] Matthews et al. (2006), [12] Andersen et al. (2019), [13] Tobin et al. (2018), [14] Massi et al. (2008), [15] Launhardt et al. (2013), [16] Andre´ et al. (2000), [17] Wiseman et al. (2001), [18] Tobin et al. (2011), [19] Sadavoy et al. (2014).

Table 2. Details of the observations a

Date Gain Polarization Antenna Flux cal. calibrator calibrator used scaling factor b

Nov 27 2018 1925+211, 0336+323, 3C 84, 0747-331 3C 454.3, 3C 84 1, 2, 3, 4, 5, 6, 7, 8 1.7 Nov 28 2018 0336+323, 3C 84, 0747-331 3C 454.3, 3C 84 2, 3, 4, 5, 6, 8 1.5 Nov 29 2018 0336+323, 0747-331, 0607-085, 0532+075 3C 454.3 3C 84 3, 4, 5, 6, 7, 8 1.4 Dec 05 2018 0336+323, 0607-085, 0532+075, 0747-331 3C 84, 3C 279, 3C 454.3 1, 3, 4, 5, 6, 8 1.2 Dec 06 2018 0336+323, 0607-085, 0532+075 3C 454.3, 3C 279 1, 3, 4, 5, 6, 8 1.3 Dec 07 2018 0532+075, 0607-085 3C 279 1, 2, 3, 4, 5, 6, 8 1.4 Apr 15 2019 1733-130, 1751+096, 1924-292, mwc349a 3C 279, 3C 273 1, 2, 3, 5, 7, 8 0.9 Apr 16 2019 1733-130, 1751+096 3C 279, 3C 273 1, 2, 3, 5, 7, 8 0.9

a Details of the observations for the first half of the sample are presented in Galametz et al. (2018). b Scaling factors derived by comparing the quasars observed with the SMA with their fluxes at similar dates in the ALMA calibration source catalog.

2.3. Data reduction, self-calibration, and flux calibration MIRIAD (Sault et al. 1995)1 for additional processing (i.e., ad- ditional flagging) and in particular to perform the instrumental We performed the data reduction on the raw visibilities us- polarization calibration. Quasars were observed to calculate the ing the IDL-based software MIR (for Millimeter Interferometer leakage terms. The continuum data of the targets were used to Reduction). The calibration includes an initial flagging of high perform an iterative self-calibration of the Stokes I visibilities. system temperatures Tsys and other incorrect visibilities, a band- The process was repeated with deeper cleans and shorter inter- pass calibration, a correction of the cross-receiver delays, and a vals until it converged (no rms improvement). We finally used gain and flux calibration. The various calibrators observed for the Atacama Large Millimeter/submillimeter Array (ALMA) each of these steps and the list of antennas used for the obser- vations are summarized in Table 2. Data were then exported to 1 https://www.cfa.harvard.edu/sma/miriad/

3 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Table 3. Characteristics of the SMA maps a

Name Synthesized beam rms in the 0.87mm reconstructed map b c I Q U Peak intensity Peak Pi p f rac (mJy/beam) (Jy/beam) (mJy/beam) %

Per B1-bS 200. 1×100. 2 (-54◦) 4.0 1.2 1.3 0.46 5.1 5.3 Per B1c 100. 8×100. 3 (-58◦) 4.0 2.3 2.4 0.44 8.2 7.5 BHR7-MMS 200. 7×100. 3 (-29◦) 2.5 1.1 1.1 0.53 4.5 0.8 HH25-MMS 100. 7×100. 5 (-67◦) 3.4 1.9 1.9 0.25 6.2 - HH211-mm 100. 5×100. 4 (71◦) 1.2 0.7 0.7 0.17 2.3 3.3 HH212 100. 7×100. 3 (-81◦) 0.6 0.2 0.2 0.19 2.1 3.0 L483-mm 100. 9 × 100. 5 (30◦) 1.6 1.3 1.2 0.10 2.7 13.6 Serpens SMM18 100. 9×100. 5 (34◦) 11.3 1.9 2.0 0.86 19.4 3.8

a Details of the SMA maps for the first half of the sample are presented in Galametz et al. (2018). b after self-calibration. c Mean polarization fraction defined as the unweighted ratio between the mean polarization over total flux. calibration source catalog2 to gather the fluxes of quasars we first detections of polarized dust emission at envelope scales to- also observed with the SMA (3C 84, 3C 454.3, 3C 273, and 3C ward BHR7 and HH25. 279) at similar dates as those of our observations. These fluxes were compared to the SMA amplitudes in order to derive the multiplying factors that were to be applied to the target visibil- 3. Analysis ity amplitude in order to flux-calibrate the dataset. These scaling 3.1. Mean magnetic field orientation factors are reported for each date in Table 2. The visibilities cov- ◦ ered by the observations range from 15 to 85 kλ. The polarization angles were rotated by 90 to obtain the magnetic field direction. The B vectors obtained for the 20 sources are overlaid on the Stokes I maps in Fig. 1. We note 2.4. Deriving the continuum and polarization maps that the strength of SMA observations is twofold. First, their The Stokes parameters are defined as interferometric nature allows us to filter out the large-scale B field permeating the surrounding host cloud, and we focus  I  on the fields in the inner protostellar envelopes. Second, the   −→ Q modest spatial resolution of our observations allows us to cancel S =   , (1) U out the more complex topology of the field at small (< 500 au) V scales because of the intense gravitational pull of the infalling material and the launching of protostellar outflows (Kwon et al. with Q and U the linear polarization and V the circular polariza- 2019). Our observations are also expected to be less prone than tion. We used a robust weighting of 0.5 to transform the visibility high-angular resolution observations to selectively tracing the data into a dirty map (using the MIRIAD invert task). We pro- B field in locations where the dust grain alignment efficiency duced cleaned images of the various Stokes parameters (using may be highly inhomogeneous, for instance, along irradiated the MIRIAD clean task). Finally, maps of the polarized intensity cavity walls that are located very close to the central protostellar (debiased) Pi, polarization fraction pfrac , and polarization angle objects (see, e.g., Le Gouellec et al. 2019). Because most Class P.A. were produced (using the MIRIAD impol task) as follows: 0 disks only contribute at scales much smaller than the scales q probed by our beam (fewer than 25% of the Class 0 disks extend 2 2 2 Pi = Q + U − σQ,U , (2) beyond 60 au; see Maury et al. 2019), dust polarization due to self-scattering is unlikely to contribute to the polarization p f rac = Pi / I, (3) observed at envelope scales with the SMA. To trace the main direction of B at envelope scales, we ex- P.A. = 0.5 × arctan(U/Q), (4) tracted the mean B-field orientation within the central 1000 au with σQ,U the average rms of the Q and U maps. We applied a 5σ region of each source. To perform the calculation, we used the cutoff on Stokes I and a 3σ cutoff on Stokes Q and U in order polarization angle and polarization angle error maps produced to only discuss locations where polarized emission is robustly with our data-reduction procedure within the idl/wmean func- detected. The synthesized beams and rms of the various cleaned tion. The weighted mean is calculated as maps are provided in Table 3. Maps are produced with a pixel 00 2 size of 0.6 . In the appendix (see Table B.1), we show that this Σxi/σ µ = i , (5) choice does not affect the mean B-field orientation we derived. Σ1/σ2 The Stokes I dust continuum emission maps are shown in i Fig. 1. A description of the morphology of this continuum emis- with µ the mean position angle of the B field, xi the individual sion as well as details of the source multiplicity are provided in position angles detected within the central 1000 au region, and Appendix A. The polarized intensity and polarization fraction σi their associated errors. We report the magnetic field position maps are shown in Fig. D.1. To our knowledge, we present the angles in Table 4 and overlay them (with red segments) on the Stokes I maps for the full sample in Fig. 2. The errors provided 2 https://almascience.eso.org/sc/ in Table 4 are the external uncertainties eu based on the spread

4 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

B1-b B1-c B335 BHR7

CB230 HH25-MMS HH211-mm HH212

HH797 IRAS03282 IRAS16293 L1157

L1448C L1448N-B L1448-2A L483-mm

IRAS4A IRAS4B SSMM18 SVS13-B

Fig. 1. B-field vectors (derived from the polarization vectors assuming a 90◦ rotation) overlaid as orange segments on the SMA 850 µm Stokes I continuum maps. Color scales are in Jy/beam. Contours at -3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 σ appear in blue. The filled ellipses in the lower left corner indicate the synthesized beam of the SMA maps.

of the values obtained multiplying the internal uncertainty iu by This method is appropriate for calculating a mean B-field the square-root of the reduced chi-squared, with angle recovered at 1000 au scales in protostellar envelopes, from individual detections presenting a large dynamic range in 1 signal-to-noise ratios, as are some of the polarization detections iu = q (6) Σ1/σ2 in the SMA map of each individual source, but also to propagate i the individual errors and angle dispersions into an error on the and mean value. While most protostars show small dispersions of their individual detections around the mean B field (18 sources r χ2 (x − µ)2 out of 20 have dispersions <20◦), we note that two protostars eu = iu where χ2 = Σ i . (7) − 2 (IRAS16293A and Per-B1c) present large angle dispersions N 1 σi

5 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

B1b B1c B335 BHR7 CB230

HH25 HH211 HH212 HH797 I03282

IRAS16293 L1157 L1448C L1448N-B L1448-2A

L483 IRAS4A IRAS4B SSMM18 SVS13-B

Fig. 2. Mean magnetic field orientation in the 20 Class 0 protostellar envelopes (red segments) overlaid on the dust emission maps (contour and color maps). Contours are indicated for detections at 5, 20, 50, and 100 σ. The common physical scale of each map is 8000 × 8000 au. We indicate the outflow axis for each source with cyan arrows. For L1448C, we report the central 2-σ detection (see Galametz et al. 2018, and §3.1.). around their mean position angle. larized emission. The three additional methods rely on (i) a simple averaging (no weighting), (ii) an averaging of the Stokes To quantify the effect of the pixel size that we used during values before computing an angle (e.g., used in the single-dish the map-making procedure on the mean B-field orientation, we maps of clouds by Li et al. 2006), or (iii) summing individual rederived the polarization maps for pixels equal to 0.600 (our Stokes fluxes to remove the variations around a mean value fiducial pixel scale), 0.700 , 0.800 , 0.900 , and 1.000 and reesti- (considering that Stokes Q and U are positive and negative, mated the mean magnetic field position angles (see Table B.1). their sum cancels most variations and should converge toward We observe that the pixel size affects the position angles we the most widespread value in the map). This second test shows derived only very little; the uncertainties on the orientation that the position angle of the mean B field computed with the are mostly dominated by the dispersion of the position angles different methods presents only small variations in the mean within the 1000 au central region. We note that for HH211, the position angle, with a dispersion smaller than the error bars interval of values obtained by changing the pixel size ranges from our method reported in Table 4. This indicates that our from 162◦ to 175◦: the error in position angle may be closer to measurement are robust envelope-scale values. One exception 10◦ than the 5◦ we report in Table 4 for this source. is HH212, for which the interval of values obtained using the various methods ranges from 51 to 59◦. As for HH211, the error Additionally, because other methods have been devel- on position angle may be closer to 10◦ than the 4◦ error reported oped for calculating mean polarization angles, we propose in in Table 4 for this source. Appendix C a simple comparison between the mean angles obtained from our method and three other averaging methods The magnetic field orientation of 12 sources of the sample that are used to analyze single-dish observations of dust po- is discussed in Galametz et al. (2018). We add here additional

6 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars notes concerning the choices we made in the current analysis. ting technique. The velocity map is shown in the appendix in For IRAS4B, the B field is complex, with an average B-field Fig. E.1. direction in the eastern part of 149±45◦ and an average direction . in the western part of 51±19◦. Both sides give a misalignment CB230, HH211-mm, IRAS03282, and L483 For these sources, ◦ 2D velocity gradients and position angles on similar scales have with the outflow of 30-50 . In this analysis, we used a misalign- + ment of 40◦ for this source. The B-field orientation used for been estimated in Tobin et al. (2011) using the N2H line and fitting a plane to the entire velocity field (with R > 1000 for L483 IRAS03292 is the average value detected in the off-centered 00 region where B is detected by the SMA (see Galametz et al. and R of about 20-25 for the other sources). We use their veloc- ity gradients and position angles in the following analysis (see 2018). In the case of L1448C, the only robust detections (>3-σ) their Table 10). L1157 is also part of their sample, with a greater are vectors located outside the central 1000 au region, as shown velocity gradient strength (from 3.5 to 10.5 km s−1 pc−1) than in our Fig. 1. For this analysis, we thus decided to report the 2-σ was derived in Gaudel et al. (2020) (0.8 km s−1 pc−1) and dif- detection of the polarized dust emission in the central region from Galametz et al. (2018): its position angle is in agreement ferent position angles depending on the use of PdBI, Combined with the 1.3 mm B-field detections reported by Hull et al. (2014) Array for Research in Millimeter-wave Astronomy (CARMA), ◦ or Very Large Array (VLA) data. We kept the values from (e.g. a P.A. of 95 ). We stress that the B-field topology in the + outer envelope layers may be complex (Cox et al. 2018) and Gaudel et al. (2020) in this paper, but recall that the N2H ve- differ from the main B-field reported here. For L1448-2A, the locity field is extremely complex for this source: the velocity hourglass shape is resolved with the SMA: we therefore used the gradient direction is close to the outflow axis, but the symmetry is perturbed by a redshifted line emission southeast of the proto- central vector detected in the TADPOL survey (Hull et al. 2014). star, with potential contribution of the outflow cavity walls to the Finally, for IRAS16293-A, we estimated the mean magnetic N H+ emission for this source (Tobin et al. 2011; Gaudel et al. field orientation in a smaller (300 in radius) aperture to avoid 2 2020). contamination by the companion source IRAS16293-B. The average value (173±40◦) is consistent with the NS orientation Per B1-bS. We calculated the 2D velocity gradients from the + also found in Rao et al. (2009), and the uncertainty is large. N2D datacube obtained from N. Hirano and presented in Huang & Hirano (2013). Compared to its companion source B1-bN, the −1 We provide details of the magnetic field orientation of the B1-bS line profiles are dominated by the VLS R= 6.3 km s com- additional eight sources in Appendix A. Most of the additional ponent. We fit this hyperfine structure with the hfs cube proce- sources present misaligned configurations between the B and dure (Estalella 2017), fitting the line when detected at a 5σ level. outflow position angles. For B1-bS, we note that we decided The procedure returns a velocity map from which we determined to use the average north-east value for our analysis because the gradient on a 2000 × 2000 region around the source to avoid apparently it better traces the magnetic field at envelope scales contamination by the companion. The map of the gas velocities connected with the field traced on larger scales. For L483, in the envelope of B1-bS that we used to extract the main veloc- the eastern line segment shows a discrepancy with the global ity gradient in this source is shown in Fig. E.1. Because a smaller orientation of the western line segments: we did not include it region was fit, the magnitude of the velocity gradient might only in our analysis (see the discussion in Appendix A, which shows provide an upper limit for this source: velocity gradients tend that this choice does not affect the correlation we find, however). to increase when probed at smaller physical radii, as shown, for instance, by Gaudel et al. (2020) (their Table 2). Finally, Table 4 also provides the outflow position angles re- Per B1-c. We calculated the 2D velocity gradients from the trieved from the literature (see references in the table). The out- + flow position angle uncertainties can vary from one source to an- N2H velocity map obtained from B. Matthews and presented other and depend on the outflow inclination and potential overlap in Matthews et al. (2006). As explained in their analysis, the of the red- and blueshifted components. We assumed a conser- spectral resolution was not sufficient to separate the hyperfine ◦ splitting components, therefore the moment map was taken over vative 10 error on the outflow position angle for all sources. + an isolated line component of N2H . The velocity map of this source is presented in Fig. E.1. We fit the velocity gradient in a 00 00 + 3.2. Kinematic properties of the protostellar envelopes 20 × 20 region around the source to encompass the full N2H emission presented in Matthews et al. (2006) (their Fig. 8). As The CALYPSO sources. For sources that are part of the for Per B1-bS, the magnitude of the velocity gradient might pro- CALYPSO sample (i.e., L1157, L1448C, L1448N-B, L1448- vide an upper limit for this source because a smaller region was 2A, IRAS4A, IRAS4B, and SVS13-B), Gaudel et al. (2020) re- fit. cently presented observations of the dense gas kinematics us- 18 + ing C O and N2H measurements. They derived specific angu- BHR7-MMS. We calculated the 2D velocity gradients from + lar momentum estimates throughout their collapsing protostel- both the H2CO and N2D datacubes obtained from J. Tobin and lar envelopes from 50 au to 10000 au scales. In their analysis, presented in Tobin et al. (2018). We used Gaussian line pro- velocity maps are produced from a combined Plateau de Bure files to model the H2CO emission and the hfs cube procedure + + (PdBI) + 30-m N2H dataset. A hyperfine structure line profile (Estalella 2017), fitting the hyperfine structure of the N2D line was used to determine the velocity of the molecular line emis- when detected at a 5σ level. For H2CO, as there is no robust de- sion in order to produce a velocity map. Then velocity gradients tection beyond a radius of 700 (equivalent to 3000 au for BHR7), were fit in a 4000 × 4000 region around the sources and deter- we estimated the velocity gradient in a 1400 × 1400 region around −1 −1 mined by the least-squares minimization, with vgrad = v0 + a∆α the source and obtained a gradient of 40 km s pc . We note, + b∆β, with ∆α and ∆β the offsets with respect to the central however, that in the cold envelope, there might not be enough source (Goodman et al. 1993). Serp SMM18 is also part of the CO in the gas phase to form H2CO: a significant part of the CALYPSO sample but is not included in the sample studied in H2CO emission could thus come from warmer gas belonging Gaudel et al. (2020). For this source, we determined the veloc- to the outflow, as suggested by the position angle (-19◦, thus ity gradient strength and position angle using the same 2D fit- aligned with the outflow) of the velocity gradient we derive. In

7 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Table 4. Position angles of the outflow and magnetic field and velocity gradient characteristics

Name Outflow Bmean Line used Velocity gradients

P.A. a Ref. P.A. Gradient P.A. Ref. (◦)(◦) (km s−1pc−1)(◦)

+ Per B1-bS 120 [1] 26±7 N2D 23±3 -8±8 [26] & T. w. + Per B1c 125 [2] 99±39 N2H 7.5 50 [2] & T. w. + B335 90 [3] 55±3 N2H ∼1.0 - [24] + BHR7-MMS 174 [4] 87±19 N2D 14±1.0 -36±6 [4] & T. w. + CB230 172 [5] 85±4 N2H 3±0.1 98±1.3 [21] HH25-MMS - [6] 74±17 - - - - + HH211-mm 116 [7] 174±5 N2H 7±0.03 26±0.3 [21,23] HH212 23 [8] 51±4 NH3 4.5 113 [22] HH797 150 [9] 110±7 - - - - + IRAS03282 120 [10] 43±6 N2H 9±0.01 114±0.01 [21] IRAS16293-A 75 & 145 [11] 173±40 CN 25 - [25] + L1157 146 [12] 149±4 N2H 0.8±0.4 113±65 [20] + L1448C 162 [13] 95±4 N2H 13±1 -179±1.0 [20] + L1448N-B 105 [14] 23±4 N2H 13±1 100±1 [20] b + L1448-2A 134 [5] 139±9 N2H 2±1 -177±21 [20] + L483 105 [15] 8±11 N2H 9±0.03 45±0.2 [21] + NGC 1333 IRAS4A 20 [16] 55±13 N2H 7±1 37±2 [20] + NGC 1333 IRAS4B 0 [17] 51±19 N2H 3±1 -71±14 [20] + Serp SMM18 8 [18] 84±16 N2H 12±0.01 69±0.04 T. w. + SVS13-B 160 [19] 18±5 N2H 5±1 16±4 [20]

a Position angles in the table are provided east of north. b Taken from Hull et al. (2013). References - T. w. refers to this work, [1] Gerin et al. (2015), [2] Matthews et al. (2008), [3] Hirano et al. (1988), [4] Tobin et al. (2018), [5] Hull et al. (2013), [6] Dunham et al. (2014), [7] Gueth & Guilloteau (1999), [8] Lee et al. (2017), [9] Tafalla et al. (2006), [10] Hatchell et al. (2007), [11] Rao et al. (2009), [12] Bachiller et al. (2001), [13] Dutrey et al. (1997), [14] Kwon et al. (2006), [15] Oya et al. (2018), [16] Choi et al. (2006), [17] Choi (2001), [18] Maury et al. (2019), [19] Bachiller et al. (1998), [20] Gaudel et al. (2020), [21] Tobin et al. (2011), [22] Wiseman et al. (2001), [23] Tanner & Arce (2011), [24] Saito et al. (1999), [25] Antonio Hernandez-G´ omez’s` PhD thesis, private communication. [26] Huang & Hirano (2013).

+ this respect, the N2D emission might better trace the gas kine- We did not analyze the position angle of the velocity gradient + matics in the envelope. The velocity map derived from the N2D for this source. datacube is presented in Fig. E.1. Using these data over a 3000 × 3000 region (equivalent to the ±2000 regions used for the Perseus HH212 and IRAS16293-A. The remaining velocity gradients sources), we obtain a weaker but still strong velocity gradient were directly taken from the literature or were obtained from −1 −1 private communication. For HH212, Wiseman et al. (2001) de- of ∼15 km s pc . We chose to use this measurement in the −1 −1 remaining analysis. termined a velocity gradient of about 4–5 km s pc over a 25–3000 region. For IRAS16293, the gradient calculated from the H13CO+ velocity map of Rao et al. (2009) is huge (430 B335. B335 is a particular case; very little rotation is observed km s−1 pc−1) and covers the whole IRAS16293-A/IRAS16293- in the source. Menten et al. (1984) only reported a velocity shift B system. ALMA and SMA are both observing this large ve- from NH observations of a few 10−2 km s−1 over half an arcmin 3 locity gradient that might be partly contaminated by the various scale, which was confirmed by the weak velocity gradient esti- outflows emerging from this complex system. When CN obser- mated by Caselli et al. (2002). Based on Saito et al. (1999) (their vations are used (Antonio Hernandez-G´ omez’s´ PhD thesis3, pri- Fig 5), we derive a velocity gradient of 1 km s−1 pc−1 over the vate communication), then the velocity gradient observed per- interval ±6000 (equivalent to the ±2000 regions used in Perseus) pendicular to the main EW outflow decreases to 25 km s−1 pc−1. in the NS direction (i.e., perpendicular to the outflow). A recent We use this value in the paper. study by Watson (2020), based on the reflection nebulosity of a nearby star, suggests that the distance to B335 could be 165 pc (we use 100 pc in this study). This greater distance, although it does not affect the mean B-field position angle derived for the source much, would lead to a velocity gradient about a factor of 2 lower than we used in this analysis. We note that there is still HH25-MMS and HH797. Finally, we were unable to find ob- much uncertainty in the position angle of the velocity gradient servations for HH25 that would allow us to estimate a velocity for this source; the C18O velocity gradient is tilted by 18◦ with respect to the east-west outflow direction (Yen et al. 2015a,b). 3 https://tel.archives-ouvertes.fr/tel-02492210/

8 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

IRAS16293A B1b

L1448N-B BHR7 L1448C 1 SSMM18 L483 10 B1c IRAS4A IRAS03282 HH212 SVS13-B HH211 IRAS4B CB230 L1448-2A

B335 100 L1157

Velocity gradient (km/s/pc) R=0.68

0 20 40 60 80 100 Misalignment B

Fig. 3. Projected angle between the mean magnetic field within the 1000 au central region and the outflow direction as a function of the velocity gradient of the source estimated from line measurements. Sources are color-coded as a function of their fragmentation below 5000 au scales (with red, light blue, and dark blue for sources with a detection of a single, double, and 3-4 dust peaks). For certain sources, two colors are used: For L483, the ALMA 1.2 mm map from Oya et al. (2017) revealed a continuum source detected at a 5σ level in the south-west region that might suggest fragmentation. For HH211, Lee et al. (2009) detected a companion source with the SMA in the southwestern extension of the source, but VLA and ALMA observations have questioned the binary nature of the source (Tobin et al. 2016; Lee et al. 2019). In both cases, the nature of the additional source needs to be better investigated to be confirmed or refuted as a companion. Finally, the companion to CB230-A appears to host two near-IR objects, thus could be part of a triple system (Massi et al. 2008). For this source, we also indicate both the velocity gradient derived by Tobin et al. (2011) from a 1D fit perpendicular to the outflow direction (empty symbol) and a 2D fit of the total velocity field (filled symbol) because the two measurements lead to different values of the velocity gradient. gradient. Although it is located in the window of observations, 4. Discussion the H13CO+ line is unfortunately not detected in this object by SMA. For HH797, the complex velocity pattern derived from the 4.1. Misaligned B fields associated with the small angular C18O datacube from Palau et al. (2014) did not allow us to esti- momentum of the protostellar gas mate a clean velocity gradient strength or direction. We decided Galametz et al. (2018) qualitatively noted a higher occurrence of to drop these two sources for the remaining analysis. misaligned B-field lines in sources in which large velocity gradi- ents were detected in the equatorial plane at scales of thousands The velocity gradient strengths (in km s−1 pc−1) and position of au. The measurements of the envelope kinematics combined angles used in this analysis are summarized in Table 4. The with B position angle measurements allow us to quantify the re- bulk of the velocity gradients resides in the [0–20] km s−1 pc−1 lation. In Fig. 3 we show the projected angle between the B-field range. This range is consistent with that derived for a sample orientation and the outflow axis as a function of the velocity gra- −1 −1 of 17 nearby protostellar systems by Tobin et al. (2011) (their dient (in km s pc ) that we used as a proxy to probe the gas Fig. 26 right). We note that velocity gradients aligned in the dynamics in the surrounding envelope. Errors on the misalign- equatorial plane are commonly interpreted as envelope rotation. ment angles (x-axis) are the addition of the B-field orientation Recent analyses have revealed a more complex interpretation, error quoted in Table 4 and that of the outflow position angle with sources showing shifts or even reversal of the gas veloc- error. The colors used in the plot are discussed in § 4.2. ity gradients within envelopes. In some sources, the observed We observe a reasonably good (R=0.68) positive correlation gradients might even originate from ongoing infall or be linked between the misalignment of B with respect to the outflow with turbulence (Gaudel et al. 2020). In all cases, however, large and the strength of the velocity gradient traced at envelope velocity gradients trace more dynamical envelopes with higher scales. This quantitatively demonstrates that a relation exists kinetic energy. between the orientation of the magnetic field and the kinematic energy in envelopes. This is consistent with the result presented in Yen et al. (2015a) and based on a sample of 17 Class 0 and I protostars where no source with large specific angular momenta were found with a strongly aligned configuration. The

9 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

log velocity gradient (km/s/pc) log velocity gradient (km/s/pc) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75

180 B1b 180 B1b

160 160 BHR7 BHR7 140 140

120 IRAS03282 HH212 L1157 120 HH212 IRAS03282 L1157 IRAS4B IRAS4B CB230 L1448N-B CB230 100 L1448N-B 100

80 80 SSMM18 SSMM18

60 B1c 60 B1c L483 L483 40 IRAS4A 40 IRAS4A

Vel. Grad. position angle HH211 Vel. Grad. position angle HH211 20 SVS13-B 20 SVS13-B L1448C L1448-2A L1448-2A L1448C 0 0 0 25 50 75 100 125 150 175 0 25 50 75 100 125 150 175 B position angle Outflow position angle

5 5

4 4

3 3

2 2 Number Number

1 1

0 0 0 20 40 60 80 0 20 40 60 80 B - Vel. Gradient P.A. (degrees) Outflow - Vel. Gradient P.A. (degrees)

Fig. 4. Top left: Velocity gradient position angle as a function of the mean magnetic field position angle. The light and darker blue stripes indicate a projected angle between the two smaller than 20 and 10◦ , respectively. The dashed line indicates a difference of 45◦ between the two position angles. Protostars are color-coded as a function of their velocity gradient, with increasing gradients as the color darkens. Top right: Relation between the velocity gradient position angle and the outflow direction. We use the same convention for the stripes and lines. We note that the blue regions indicate sources whose velocity gradient might partly be tracing the outflow motion rather than the envelope motions. Bottom: Corresponding histograms of the misalignment of (left) the B field and (right) the outflow axis with respect to the velocity gradient position angle. Colors and lines delineate the same angle offsets as in the top panels. correlation observed in Fig. 3 may be interpreted in various dashed line indicates a difference of 45◦ between the two posi- ways. One interpretation might be that the misalignments of B tion angles. We color-code sources as a function of the velocity at envelope scales are driven by the strong rotational or infall gradient strength. The bottom left panel shows the corresponding motions of the envelope, while another interpretation might be histogram of the angular difference between the position angle that an aligned B field could have favored the smaller velocity of B and the velocity gradient position angle. gradients we observe. We observe that regardless of the height (so potentially ef- fect) of the velocity gradient, we do not observe an alignment If the misalignment of B with respect to the outflow at enve- of the magnetic field direction and the velocity gradient posi- lope scales were driven by the envelope kinematics (i.e., if the tion angle. This suggests that the B-field lines do not preferen- initially aligned B-field lines were to be twisted by the infalling tially follow the direction of the matter infall and collapse dy- or rotating matter), we would expect a relation of the position namics. On the contrary, the sources seem to be scattered across angle of B and that of the velocity gradient. We plot the velocity the plot, as highlighted by the relatively flat corresponding his- gradient position angle as a function of the mean magnetic field togram (Fig. 4 bottom left). This could indicate that the corre- position angle in Fig. 4 (left). To facilitate visualization, the light lation observed in Fig. 3 has a more complex explanation than and darker stripes indicate where the projected angle between matter infall or rotation that causes the misaligned magnetic field the two directions is smaller than 20 and 10◦ , respectively. The lines. This could favor the second interpretation, namely that in

10 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars sources showing an aligned configuration of B, magnetic braking the two sources SVS13-B and IRAS4B have large-scale com- could be more efficient at removing angular momentum, leading panions (SVS13-A and IRAS4B2 located at 4200 au and 3200 to the smaller velocity gradient we observe. au from SVS13-B and IRAS4B1, respectively), but they do not Reinforcing the interpretation that the correlation may be due seem to be fragmented below 3000 au scales, to our knowledge. to more efficient magnetic braking at removing angular momen- These sources have moderate velocity gradients and B is mis- tum in sources initially in an aligned configuration of B further, aligned, so they are both located in the bottom left quadrant of we stress that most sources with low values of their envelope Fig. 3. When our separation criterion is whether fragmentation gas velocity gradient also have an envelope B field that is well is observed above and below 3000 au scales (compared to 5000 aligned with the field observed in their surrounding environment. au scales as before), the p-value of the previous K-S test drops The large-scale magnetic field lines probed around L1157 by to 0.04, which is also consistent with our conclusion that a di- Planck or probed at intermediate scales with SHARP (Stephens chotomy exists between the single versus multiple source popu- et al. 2013; Chapman et al. 2013) are consistent with the SMA lation and that the magnetic field alignment might affect the way B orientation. We note that results from optical polarimetry are in which the envelope fragments. also consistent, with a small angle offset <20◦ (Sharma et al. Observational studies have suggested that the magnetic field 2020). For B335, the orientation of the near-IR polarization vec- might affect the fragmentation rate at molecular clouds or fila- tors seems to also fit with the orientation of the submillimeter po- ments scales (e.g., Teixeira et al. 2016; Koch et al. 2018). Our larization vectors (Bertrang et al. 2014) and with the east-west analysis at protostellar envelope scales appears to support the direction found with JCMT-POL by Yen et al. (2019). Finally, theoretical predictions that the magnetic field orientation in the the B-field lines in NGC 1333 IRAS4A, HH211, or L1448- envelope also plays a role in favoring or inhibiting the fragmen- 2A appear to be extremely well ordered at scales traced by the tation processes of a dense protostellar core into multiple sys- SHARP or SCUBA instruments (Hull et al. 2014, see) down tems. We further discuss the predictions from MHD simulations to the SMA scales. B1-c does not follow this trend, however, and their relation to our results in the following section. with a large-scale B field oriented with a position angle of 35◦ (Matthews & Wilson 2002), that is, nearly perpendicular to the outflow direction, compared to the SMA 100◦ orientation. 4.3. Consistency with predictions from MHD simulations The nature of the gas kinematics recovered at these envelope In ideal MHD models, B fields are shown to strongly regulate scales (i.e., whether the angular momentum originates from ro- the transport of angular momentum and hence modify the final tation, infall, or even from turbulent motions inherited from the properties of stars and disks (see Hennebelle & Inutsuka 2019; initial conditions and/or turbulence), is unknown. Its amount ap- Wurster & Li 2018; Zhao et al. 2020, and references therein). pears to be intimately linked to the magnetic configuration in The inclusion of more realistic non-ideal MHD effects changed protostellar envelopes, however. this view, with finer effects that may play a crucial role regarding the ability of B to interact with gas kinematics, such as ioniza- tion and dust properties (Zhao et al. 2018). Some studies have 4.2. Indication of higher multiplicity in systems with shown that B is in particular less efficient at transporting angular misaligned magnetic fields ? momentum when it is initially misaligned with the rotation of In order to investigate the effect of the magnetic field on the en- the system (Joos et al. 2012). velope fragmentation, we color-code the sources of Fig. 3 de- That a link might exist between the initial core-scale mag- pending on whether they are fragmented below 5000 au scales. netic field orientation with respect to the rotation axis that drives We indicate in particular whether the source hosts a single, dou- the small-scale outflow launching and fragmentation has been ble, triple, or quadruple dust peak (using submillimeter direct predicted by models of protostellar formation. Through the col- imaging). Details of the fragmentation for each individual source lapse of a dense rotating infalling core and in the extreme case of are provided in Appendix A. We stress that very close multiplic- an envelope rotation axis initially perpendicular to the magnetic ity (below 100 au scales) is not considered in our analysis. field, Price & Bate (2007) have shown, for instance, that the We observe that sources standing as single objects (in red) magnetic tension appears to play an even more significant role mostly appear to reside in the bottom left corner of the plot, that in helping fragmentation. Inserting magnetic fields also appears is, with relatively small velocity gradients of their surrounding to be a necessary condition to reproduce the fragmentation rates envelopes and aligned magnetic field orientation with respect now observed in massive cores with ALMA, as suggested by to the outflow axis. Uncertainties also remain about the nature Fontani et al. (2016). The observations provide information of potential companions detected in HH211 and L483, hence of the main field direction at envelope scales: in an aligned these sources appear with two colors in Fig. 3. In order to as- configuration, thus more organized magnetic field configuration, sess whether the two populations (single versus multiple) belong the magnetic pressure will be more efficient at stabilizing to the same distribution, we applied a 2D Kolmogorov-Smirnov the envelope, reducing the rotation-induced fragmentation at test. We used the two python scripts ndtest.py4 and KS2D.py5 to comparable scales (i.e., below 5000 au scales). If fragmentation estimate the K-S statistics and p-values. These 2D testings are were favored by less efficient magnetic braking processes, it based on statistical methods developed by Peacock (1983) and could also be enhanced by ‘turbulent’ fragmentation, that is, Fasano & Franceschini (1987). Excluding the sources for which fragmentation linked to the increase of the kinematic energy of the exact multiplicity nature is unsure (i.e., HH211 and L483), envelopes in misaligned configurations. Following our observa- both methods return the same low p-value of 0.13, indicating tional results, a study of non-ideal MHD models of protostellar that the single and multiple source populations likely do not collapse that searched for the roots of the correlation we report belong to the same population. More sources would, however, was initiated and is currently carried out by the team. be necessary to reinforce this statistical test. We also note that The question is whether a potential effect of the misaligned 4 https://github.com/syrte/ndtest/blob/master/ndtest.py B-field orientation on the final protostellar disk sizes might be 5 https://github.com/Gabinou/2DKS/blob/master/KS2D.py observed. If less angular momentum is transported from the en-

11 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars velope to the disk scales in the case of B-aligned configuration, 90 as suggested by our study at envelope scales, smaller rotation- 80 3.0% supported disks are expected. Observationally, the small size of 70 disks in some Class 0 protostars has been interpreted as a con- 2.5% sequence of an efficient magnetic braking that potentially dis- 60 rupts the disk formation (Maury et al. 2010; Yen et al. 2015a; 2.0% Segura-Cox et al. 2018). Magnetohydrodynamics simulations 50 from Hirano et al. (2020) recently confirmed that in the later 40 1.5% accretion phase, the smallest disk radius and mass are produced

Observed angle 30 in alignment-configuration cases. Using the CALYPSO sample, 1.0% Maury et al. (2019) have shown that fewer than 25% of the 26 20 0.5% Class 0 protostars may harbor large protostellar disks resolved 10 at radii >60 au. Their results also favor a magnetized scenario 0 0.0% for the disk formation. Unfortunately, most sources with large 0 10 20 30 40 50 60 70 80 90 disk-like structures (L1527, SMM4, MM22, and GF9-2) are not Real angle included in the current sample. The disk sizes are mostly unre- Fig. 5. Monte Carlo test for 10000 randomly generated vector solved at ∼50 au scales in the remaining sources of our sample pairs projected onto a 3D plane mimicking the plane of the sky. that overlap with the CALYPSO sample. This prevents us from This plot shows the density distribution of the angles obtained studying the effect of the B misalignment on the disk forma- by projecting these vector pairs onto the plane compared to their tion itself. Such studies are currently hampered by the need of real angle separation in 3D. The color bar indicates the probabil- very high spatial resolution to study these disks with ALMA, for ities of each projected vs. true angle pair. instance. Recent ALMA results from Cox et al. (2018) have ana- lyzed, for instance, the polarization angle dispersion and tried to connect the signature or randomness of the B field with the disk or non-disk nature of their sources. The extremely complex mor- angles between the various directions analyzed (velocity gradi- phology of magnetic fields in Class 0 protostars observed with ents, B, and outflows). In order to assess the uncertainties linked ALMA at 50 au typical disk scales may suggest a less dynami- with projection effects, we performed a Monte Carlo test. We cally relevant B field at these scales, as expected from non-ideal developed a python script that randomly generates a 3D plane. MHD models (e.g., with ambipolar diffusion leading to a weaker This plane was our plane of the sky. We then generated 10000 coupling of the magnetic field lines with the circumstellar gas; random pairs of vectors in this 3D space. For each pair, vectors Mellon & Li 2009; Tsukamoto et al. 2015). We stress, however, were projected onto the 3D plane (using the orthogonal basis that the characterization of B in disks remains problematic, as of the plane) to estimate the two ‘projected vectors’ and thus several mechanisms can contribute to the production of polar- ‘observed angle’ between the two. The ‘real’ and ‘observed’ an- ized dust emission at these scales (Kataoka et al. 2015; Cox et al. gles were then compared. Figure 5 shows the density distribution 2018). of the observed versus real angles. The 2D density plot is gen- erated with the hexbin python function (Seaborn package). For simplicity, we modified the color bar to indicate the probabilities 4.4. Assessing the various caveats of each observed-real angle pair. As expected, the projected an- 4.4.1. Outflow contamination gles are most of the time equal to (i.e., on the diagonal) or lower (i.e., on the bottom right area) than the corresponding real an- Assessing the preferential direction and strength of the mov- gle. Qualitatively, the bright diagonal highlights that we did not ing gas in protostellar envelopes is complicated by the pres- make a fundamental mistake by taking the observed angle as a ence of outflows (sometimes more than one, e.g., in the case of proxy for the real angle. IRAS16293-A) that can contribute to the observed gradients, al- To quantify the effects, we separated the ‘observed’ angles though our choice of mostly using a dense or cold gas tracer such into 18 bins of 5◦ each and provide the mean ‘real angle’ in + as N2H should largely limit the contamination. In Fig. 4 (right) Table 5. The standard deviations for each observed angle bins we plot the velocity gradient position angle as a function of the are provided as uncertainties. We note that the ‘true angle’ distri- outflow direction. The dashed line delineates a difference of 45◦ butions corresponding to each bin are not Gaussian. We observe between the two position angles. The light and darker stripes in- that the largest discrepancies between the ‘real’ and ’observed’ dicate when the projected angle between the two is smaller than angles appear for ‘observed’ angles below 40◦, with large error 20 and 10◦ , respectively, which indicates regions with sources bars. In Fig. 3, these projection effects could therefore shift the whose velocity gradient might be more related to the outflow dy- sources with a B misalignment lower than 40◦ to the right and namics than to the envelope kinematics we analyzed here. The realign these sources along a more global linear correlation be- bottom right panel of Fig. 4 provides the histogram of the mis- cause the projection effects do not strongly affect sources beyond alignement of the outflow and the gradient. The dispersion in a 40◦ misalignment. Synthetic observations derived from MHD the outflow - gradient misalignment is consistent with the results simulations are currently developed by the team to complement from Tobin et al. (2011) (their Fig. 27). For only 3 sources is the these tests on projection effects (Valdivia et al. in prep.). velocity gradient roughly aligned with the outflow direction, that is, with ∆(P.A.) < 30◦ (see Fig. 4 right). 4.4.3. Dependence on tracers One of the caveats of this analysis is also that it depends on the 4.4.2. Projection effects 18 + molecular line tracers chosen. Both C O and N2H datacubes The position and misalignment angles quoted in this analysis are are available for the CALYPSO sources. We decided to select + projected in the plane of the sky and might differ from the real N2H as a tracer of the envelope kinematics. Several analyses

12 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Table 5. Mean ‘true angle’ per ‘observed angle’ bins rather aligned B-field orientation compared to the outflow axis. Altogether, the observations tend to show a coherent picture for the role of the magnetic field in forming stars and their proto- Observed angle Mean ‘true angle’ planetary disks: they suggest that strong B fields in an aligned (◦)(◦) configuration may be more efficient in regulating both the gas kinematics and the level of fragmentation during the early em- [0 - 5] 38.8 ± 25.4 bedded phases of star and disk formation. Our findings could be [5 - 10] 36.2 ± 25.3 in line with theoretical expectation from the most recent mag- [10 - 15] 41.3 ± 24.3 netized models of star formation, which predict reduced angular [15 - 20] 38.7 ± 22.5 momentum at smaller scales due to magnetic braking, although a [20 - 25] 41.4 ± 21.6 thorough exploration of the physical causes behind the observed [25 - 30] 46.0 ± 19.7 correlations should be explored in numerical models. Our results [30 - 35] 48.3 ± 18.5 provide a strong observational confirmation of the cornerstone [35 - 40] 50.0 ± 18.8 role of B in regulating the formation of stellar systems and set- [40 - 45] 52.4 ± 16.1 tling the primordial conditions from which the future disk, star, [45 - 50] 54.6 ± 16.3 and planets will form. [50 - 55] 60.5 ± 15.0 [55 - 60] 65.5 ± 14.6 [60 - 65] 65.4 ± 14.5 Acknowledgments [65 - 70] 69.6 ± 14.0 We thank the anonymous referee for his/her constructive sug- [70 - 75] 73.4 ± 14.2 gestions that improve our methodology descriptions and over- [75 - 80] 76.6 ± 14.4 all quality of the manuscript. This project has received fund- [80 - 85] 79.1 ± 15.1 ing from the European Research Council (ERC) under the [85 - 90] 80.2 ± 14.5 European Union Horizon 2020 research and innovation pro- gramme (MagneticYSOs project, grant agreement N◦ 679937, have shown it to be a robust tracer of the outer envelopes, thus PI: Maury). J.M.G. is supported by the grant AYA2017-84390- C2-R (AEI/FEDER, UE). We thank John Tobin for providing the scales we trace with the SMA, rather than of the central re- + gions where this molecule is usually depleted and whose kine- us with the BHR7 H2CO and N2D datacubes (presented in 18 + Tobin et al. 2018). We also thank Naomi Hirano and Brenda matics gas are then usually traced through C O or H2D (Bergin + et al. 2002; Anderl et al. 2016; Gaudel et al. 2020; Maret et al. Matthews for providing us with the N2H data cubes for B1b and B1c respectively (data presented in Huang & Hirano (2013) 2020). We used the NH3 molecule for HH212: the joined analy- + and Matthews et al. (2008)). We finally thank Aina Palau for pro- sis of N2H and NH3 by Tobin et al. (2011) has confirmed that 18 both lines trace similar physical conditions at the scales we study viding us with the C O data cube for HH797 (see Palau et al. + 2014). This publication is based on data of the Submillimeter here. We also selected N2D and CN as complementary tracers of cold dense gas. Thus, unless some strongly different chem- Array. The SMA is a joint project between the Smithsonian ical effects are at work in the different protostellar envelopes, Astrophysical Observatory and the Academia Sinica Institute of all sources have been observed with homogeneous gas tracers. Astronomy and Astrophysics, and is funded by the Smithsonian Variations in the opacity from one source to another could bias Institution and the Academia Sinica. the physical scales at which the velocity gradients are probed, References + with the observed N2H arising from projected shells or more external regions than what we assumed. N H+ or N D+ could Allen, A., Li, Z.-Y., & Shu, F. H. 2003, ApJ, 599, 363 2 2 Anderl, S., Maret, S., Cabrit, S., et al. 2016, A&A, 591, A3 also be absent near the protostar, although this should not have Andersen, B. C., Stephens, I. W., Dunham, M. M., et al. 2019, ApJ, 873, 54 a strong effect on the scales probed in this analysis. A more ex- Andersson, B.-G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A, 53, 501 tended analysis using other tracers of the gas dynamics would Andre,´ P., Ward-Thompson, D., & Barsony, M. 2000, Protostars and Planets IV, help test the robustness of our conclusions at various envelope 59 Anthony-Twarog, B. J. 1982, AJ, 87, 1213 radii and/or for gas that is subject to different local conditions. Bachiller, R., Guilloteau, S., Gueth, F., et al. 1998, A&A, 339, L49 Bachiller, R., Perez´ Gutierrez,´ M., Kumar, M. S. N., & Tafalla, M. 2001, A&A, 372, 899 5. Summary Bergin, E. A., Alves, J., Huard, T., & Lada, C. J. 2002, ApJ, 570, L101 Bertrang, G., Wolf, S., & Das, H. S. 2014, A&A, 565, A94 We have carried out dust polarization observations at 0.87 mm Bontemps, S., Andre, P., & Ward-Thompson, D. 1995, A&A, 297, 98 for 20 Class 0 protostars with the SMA. We analyzed the mis- Caselli, P., Benson, P. J., Myers, P. C., & Tafalla, M. 2002, ApJ, 572, 238 Chapman, N. L., Davidson, J. A., Goldsmith, P. F., et al. 2013, ApJ, 770, 151 alignment of the magnetic field orientation (derived over the cen- Chen, X., Arce, H. G., Zhang, Q., et al. 2013, ApJ, 768, 110 tral 1000 au scales) with the outflow orientation in order to com- Choi, M. 2001, ApJ, 553, 219 pare this misalignment with the gas kinematics. The dynamics of Choi, M., Hodapp, K. W., Hayashi, M., et al. 2006, ApJ, 646, 1050 the gas was traced through measurements of velocity gradients at Ciardi, A. & Hennebelle, P. 2010, MNRAS, 409, L39 envelope scales using molecular line emission. Our analysis pro- Codella, C., Cabrit, S., Gueth, F., et al. 2014, A&A, 568, L5 Coude,´ S., Bastien, P., Houde, M., et al. 2019, ApJ, 877, 88 vides for the first time a quantification of the striking correlation Cox, E. G., Harris, R. J., Looney, L. W., et al. 2018, ApJ, 855, 92 that links the misalignment of the magnetic field orientation at Duchene,ˆ G. & Kraus, A. 2013, Annual Review of Astronomy and Astrophysics, envelope scales and the angular momentum of the gas reservoir 51, 269 that is directly involved in the star formation process. Comparing Dunham, M. M., Arce, H. G., Mardones, D., et al. 2014, ApJ, 783, 29 Dutrey, A., Guilloteau, S., & Bachiller, R. 1997, A&A, 325, 758 the trend with the presence of multiple stellar systems, we also Estalella, R. 2017, PASP, 129, 025003 show that sources that tend to stand as single objects mostly Evans, II, N. J., Dunham, M. M., Jørgensen, J. K., et al. 2009, ApJS, 181, 321 reside in environments with a weak velocity gradient and/or a Fasano, G. & Franceschini, A. 1987, MNRAS, 225, 155

13 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Fontani, F., Commerc¸on, B., Giannetti, A., et al. 2016, A&A, 593, L14 Ortiz-Leon,´ G. N., Loinard, L., Dzib, S. A., et al. 2018b, ApJ, 869, L33 Galametz, M., Maury, A., Girart, J. M., et al. 2018, A&A, 616, A139 Oya, Y., Sakai, N., Watanabe, Y., et al. 2017, ApJ, 837, 174 Galli, D., Lizano, S., Shu, F. H., & Allen, A. 2006, ApJ, 647, 374 Oya, Y., Sakai, N., Watanabe, Y., et al. 2018, ApJ, 863, 72 Gaudel, M., Maury, A. J., Belloche, A., et al. 2020, A&A, 637, A92 Palau, A., Zapata, L. A., Rodr´ıguez, L. F., et al. 2014, MNRAS, 444, 833 Gerin, M., Pety, J., Commerc¸on, B., et al. 2017, A&A, 606, A35 Park, Y. S., Panis, J. F., Ohashi, N., Choi, M., & Minh, Y. C. 2000, ApJ, 542, 344 Gerin, M., Pety, J., Fuente, A., et al. 2015, A&A, 577, L2 Peacock, J. A. 1983, MNRAS, 202, 615 Gibb, A. G. & Davis, C. J. 1998, MNRAS, 298, 644 Plunkett, A. L., Fernandez-L´ opez,´ M., Arce, H. G., et al. 2018, A&A, 615, A9 Girart, J. M., Estalella, R., Palau, A., Torrelles, J. M., & Rao, R. 2014, ApJ, 780, Price, D. J. & Bate, M. R. 2007, MNRAS, 377, 77 L11 Rao, R., Girart, J. M., Marrone, D. P., Lai, S.-P., & Schnee, S. 2009, ApJ, 707, Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science, 313, 812 921 Goodman, A. A., Benson, P. J., Fuller, G. A., & Myers, P. C. 1993, ApJ, 406, Sadavoy, S. I., Di Francesco, J., Andre, P., et al. 2014, ApJ, 787, L18 528 Saito, M., Sunada, K., Kawabe, R., Kitamura, Y., & Hirano, N. 1999, ApJ, 518, Gray, W. J., McKee, C. F., & Klein, R. I. 2018, MNRAS, 473, 2124 334 Gueth, F. & Guilloteau, S. 1999, A&A, 343, 571 Sault, R. J., Teuben, P. J., & Wright, M. C. H. 1995, in Astronomical Society of Hatchell, J., Fuller, G. A., & Richer, J. S. 2007, A&A, 472, 187 the Pacific Conference Series, Vol. 77, Astronomical Data Analysis Software Hennebelle, P., Commerc¸on, B., Chabrier, G., & Marchand, P. 2016, ApJ, 830, and Systems IV, ed. R. A. Shaw, H. E. Payne, & J. J. E. Hayes, 433 L8 Segura-Cox, D. M., Looney, L. W., Tobin, J. J., et al. 2018, ApJ, 866, 161 Hennebelle, P., Commerc¸on, B., Lee, Y.-N., & Charnoz, S. 2020, A&A, 635, Sharma, E., Gopinathan, M., Soam, A., et al. 2020, A&A, 639, A133 A67 Stephens, I. W., Looney, L. W., Kwon, W., et al. 2013, ApJ, 769, L15 Hennebelle, P. & Fromang, S. 2008, A&A, 477, 9 Stutz, A. M., Rubin, M., Werner, M. W., et al. 2008, ApJ, 687, 389 Hennebelle, P. & Inutsuka, S.-i. 2019, Frontiers in Astronomy and Space Sugitani, K., Nakamura, F., Watanabe, M., et al. 2011, ApJ, 734, 63 Sciences, 6, 5 Tafalla, M., Kumar, M. S. N., & Bachiller, R. 2006, A&A, 456, 179 Hennebelle, P. & Teyssier, R. 2008, A&A, 477, 25 Tanner, J. D. & Arce, H. G. 2011, ApJ, 726, 40 Herczeg, G. J., Kuhn, M. A., Zhou, X., et al. 2019, ApJ, 878, 111 Teixeira, P. S., Takahashi, S., Zapata, L. A., & Ho, P. T. P. 2016, A&A, 587, A47 Hirano, N., Kamazaki, T., Mikami, H., Ohashi, N., & Umemoto, T. 1999, in Star Terebey, S., Shu, F., & Cassen, P. 1984, ApJ, 286, 529 Formation 1999, ed. T. Nakamoto, 181–182 Tobin, J. J., Bos, S. P., Dunham, M. M., Bourke, T. L., & van der Marel, N. 2018, Hirano, N., Kameya, O., Nakayama, M., & Takakubo, K. 1988, ApJ, 327, L69 ApJ, 856, 164 Hirano, S. & Machida, M. N. 2019, MNRAS, 485, 4667 Tobin, J. J., Hartmann, L., Chiang, H.-F., et al. 2011, ApJ, 740, 45 Hirano, S., Tsukamoto, Y., Basu, S., & Machida, M. N. 2020, arXiv e-prints, Tobin, J. J., Looney, L. W., Li, Z.-Y., et al. 2016, ApJ, 818, 73 arXiv:2006.13233 Tobin, J. J., Sheehan, P. D., Megeath, S. T., et al. 2020, ApJ, 890, 130 Hsu, D. C., Ford, E. B., Ragozzine, D., & Ashby, K. 2019, AJ, 158, 109 Tsukamoto, Y., Iwasaki, K., Okuzumi, S., Machida, M. N., & Inutsuka, S. 2015, Huang, Y.-H. & Hirano, N. 2013, ApJ, 766, 131 MNRAS, 452, 278 Hull, C. L. H., Plambeck, R. L., Bolatto, A. D., et al. 2013, ApJ, 768, 159 Vallee,´ J. P. 2004, New Astronomy Reviews, 48, 763 Hull, C. L. H., Plambeck, R. L., Kwon, W., et al. 2014, ApJS, 213, 13 Cernis,ˇ K. & Straizys,ˇ V. 2003, Baltic Astronomy, 12, 301 Hull, C. L. H. & Zhang, Q. 2019, Frontiers in Astronomy and Space Sciences, Watson, D. M. 2020, Research Notes of the American Astronomical Society, 4, 6, 3 88 Joos, M., Hennebelle, P., & Ciardi, A. 2012, A&A, 543, A128 Wiseman, J., Wootten, A., Zinnecker, H., & McCaughrean, M. 2001, ApJ, 550, Jørgensen, J. K. 2004, A&A, 424, 589 L87 Kataoka, A., Muto, T., Momose, M., et al. 2015, ApJ, 809, 78 Woermann, B., Gaylard, M. J., & Otrupcek, R. 2001, MNRAS, 325, 1213 Koch, P. M., Tang, Y.-W., Chapman, N. L., et al. 2018, arXiv e-prints, Wurster, J. & Bate, M. R. 2019, MNRAS, 486, 2587 arXiv:1801.06995 Wurster, J. & Lewis, B. T. 2020, MNRAS, 495, 3807 Kwon, W., Looney, L. W., Crutcher, R. M., & Kirk, J. M. 2006, ApJ, 653, 1358 Wurster, J. & Li, Z.-Y. 2018, Frontiers in Astronomy and Space Sciences, 5, 39 Kwon, W., Stephens, I. W., Tobin, J. J., et al. 2019, ApJ, 879, 25 Yen, H.-W., Koch, P. M., Takakuwa, S., et al. 2015a, ApJ, 799, 193 Launhardt, R., Stutz, A. M., Schmiedeke, A., et al. 2013, A&A, 551, A98 Yen, H.-W., Takakuwa, S., Koch, P. M., et al. 2015b, ApJ, 812, 129 Le Gouellec, V. J. M., Hull, C. L. H., Maury, A. J., et al. 2019, ApJ, 885, 106 Yen, H.-W., Zhao, B., Hsieh, I. T., et al. 2019, ApJ, 871, 243 Lee, C.-F., Hasegawa, T. I., Hirano, N., et al. 2010, ApJ, 713, 731 Zhang, Q., Qiu, K., Girart, J. M., et al. 2014, ApJ, 792, 116 Lee, C.-F., Hirano, N., Palau, A., et al. 2009, ApJ, 699, 1584 Zhao, B., Caselli, P., Li, Z.-Y., & Krasnopolsky, R. 2018, MNRAS, 473, 4868 Lee, C.-F., Ho, P. T. P., Bourke, T. L., et al. 2008, ApJ, 685, 1026 Zhao, B., Tomida, K., Hennebelle, P., et al. 2020, Space Sci. Rev., 216, 43 Lee, C.-F., Kwon, W., Jhan, K.-S., et al. 2019, ApJ, 879, 101 Zucker, C., Speagle, J. S., Schlafly, E. F., et al. 2019, ApJ, 879, 125 Lee, C.-F., Li, Z.-Y., Ching, T.-C., Lai, S.-P., & Yang, H. 2018, ApJ, 854, 56 Lee, C.-F., Rao, R., Ching, T.-C., et al. 2014, ApJ, 797, L9 Lee, J. W. Y., Hull, C. L. H., & Offner, S. S. R. 2017, ApJ, 834, 201 Li, H., Griffin, G. S., Krejny, M., et al. 2006, ApJ, 648, 340 Marcelino, N., Gerin, M., Cernicharo, J., et al. 2018, A&A, 620, A80 Appendix A: Individual source characteristics Maret, S., Maury, A. J., Belloche, A., et al. 2020, A&A, 635, A15 Marrone, D. P. 2006, PhD thesis, Harvard University B1-bS Marrone, D. P. & Rao, R. 2008, in Proc. SPIE, Vol. 7020, Millimeter and Continuum morphology at 850 µm . When the large-scale enve- Submillimeter Detectors and Instrumentation for Astronomy IV, 70202B lope of Per B1-b is elongated in the north-south direction and en- Massi, F., Codella, C., Brand, J., di Fabrizio, L., & Wouterloot, J. G. A. 2008, A&A, 490, 1079 compasses the two sources B1-bN and B1-bS (Chen et al. 2013), Masson, J., Chabrier, G., Hennebelle, P., Vaytet, N., & Commerc¸on, B. 2016, our SMA observations only focus on B1-bS. They reveal a core A&A, 587, A32 elongated in the northwest-southeast direction at 1000-2000 au Matthews, B., Bergin, E., Crapsi, A., et al. 2008, Ap&SS, 313, 65 scales, a morphology very similar to that observed at 3mm with Matthews, B. C., Hogerheijde, M. R., Jørgensen, J. K., & Bergin, E. A. 2006, ApJ, 652, 1374 the Nobeyama Array (Hirano et al. 1999) or 850 µm with ALMA Matthews, B. C., McPhee, C. A., Fissel, L. M., & Curran, R. L. 2009, ApJS, 182, (Gerin et al. 2017). 143 Fragmentation. The two submillimeter sources in B1-b were Matthews, B. C. & Wilson, C. D. 2002, ApJ, 574, 822 first discovered by Hirano et al. (1999). The companion of Maury, A. J., Andre,´ P., Hennebelle, P., et al. 2010, A&A, 512, A40+ 00 Maury, A. J., Andre,´ P., Men’shchikov, A., Konyves,¨ V., & Bontemps, S. 2011, B1-bS is called B1-bN and is located ∼16 north. It was studied A&A, 535, A77 with the VLA by Tobin et al. (2016). The observations allowed Maury, A. J., Andre,´ P., Testi, L., et al. 2019, A&A, 621, A76 them to show that the two sources have similar temperatures, Maury, A. J., Girart, J. M., Zhang, Q., et al. 2018, MNRAS, 477, 2760 but that B1-bS is twice as luminous as B1-bN. Both sources Mellon, R. R. & Li, Z.-Y. 2009, ApJ, 698, 922 Menten, K. M., Walmsley, C. M., Kruegel, E., & Ungerechts, H. 1984, A&A, seem to be extremely different in terms of their richness in com- 137, 108 plex organic molecules (COM), as revealed by recent ALMA Olofsson, S. & Olofsson, G. 2009, A&A, 498, 455 observations (Marcelino et al. 2018). The ALMA results do not Ortiz-Leon,´ G. N., Loinard, L., Dzib, S. A., et al. 2018a, ApJ, 865, 73 reveal further fragmentation in B1-bS below 200 au scales. The

14 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars source Per-emb-41, located only 1300 in the southwest of B1-bS, the orientation of the central detection, which might be the appears to be more evolved (Tobin et al. 2016). f Magnetic signature of an hourglass morphology. field orientation. On the large scales observed by SCUBA (Matthews & Wilson 2002) or the B-fields In STar-forming HH25-MMS Region Observations (BISTRO) survey (Coude´ et al. 2019), the Continuum morphology at 850 µm. HH25-MMS is part of a B1-b system already shows strong variations in its polarization string of embedded young stellar objects (the HH24-26 com- position angle, with a mean value of the magnetic field direction plex; Bontemps et al. 1995; Gibb & Davis 1998). SMA 870 µm position angle toward B1-bS of about 30◦. This orientation is observations by Chen et al. (2013) have shown that three dis- consistent with the average B-field orientation obtained with tinct sources compose the system (SMM1, SMM2, and SMM3) the SMA in the northeast region (26◦). The western vectors and are aligned in the north-south direction. If SMM1 were the are oriented at 111◦, that is, perpendicular to the eastern vector driving source of the HH25 outflow, the SMA polarization data and along the outflow direction. We decided to use the average focus on the SMM2 source. Its SMA continuum appears to be northeast value for this analysis because it appears to trace extended in the east-west direction. the magnetic field better at envelope scales connected with the Fragmentation. As mentioned previously, SMM2 is part of a magnetic field traced on larger scales. three-source system, with separations of 13 and 1100 with SMM1 and SMM3, respectively. On larger scales, HH25-MMS also has B1-c a Class I companion, HH26IR, located 1.50 to the southwest. Continuum morphology at 850 µm. The large-scale 2.7 and 3.3 Magnetic field orientation. Elongated in the north-south di- mm continuum emission observed by Matthews et al. (2006) rection, the HH25-MMS system is separated into three distinct presents extensions mostly along the outflow. In contrast, the 850 sources (SMM1, SMM2, and SMM3) resolved by Chen et al. µm SMA continuum is flattened in the direction perpendicular to (2013). The SMA observation focuses on SMM2. This is the the source outflow. This is consistent with the SMA 1.3 mm dust first known detection of polarized dust emission toward this continuum image presented in Chen et al. (2013). The northern source. However, we do not detect polarization toward the very and southwestern plumes are also observed with ALMA at 870 central region but in its western extension. The magnetic field µm (see Cox et al. 2018). at this position is tilted in the 74◦ direction, that is, mainly Fragmentation. The source is a single source at the SMA scales perpendicular to the projected line connecting the three sources. (this work), at the VLA scales probed by the VLA/ALMA In this analysis, we did not compare the B-field orientation Nascent Disk and Multiplicity (VANDAM) survey (Tobin et al. with the known outflow of the region (revealed by a VLA 3.6 2016), and at the ALMA scales probed by Cox et al. (2018). cm survey) because there is strong evidence that the outflow originates from SMM1 and not from SMM2 (Bontemps et al. Magnetic field orientation. At the large scales observed by 1995; Chen et al. 2013). SCUBA (Matthews & Wilson 2002), B1-c has a polarization ◦ angle at 35 , that is, a magnetic field nearly perpendicular to HH211-mm the outflow direction (estimated at -55◦; Matthews et al. 2006). Matthews et al. (2008) and the results from the BISTRO survey Continuum morphology at 850 µm. As observed at 230 GHz (Coude´ et al. 2019) revealed a more complex pattern. Our by Gueth & Guilloteau (1999), the HH211-mm submm contin- SMA results are consistent with these more recent results: the uum emission is compact. Also resolved with the SMA, the con- SMA northern vectors are oriented at an angle of 152◦ and the tinuum is slightly elongated in the southwest direction, that is, central vectors are oriented in an east-west orientation, with perpendicular to the outflow axis. an average in position angle of 70◦. The average in the central Fragmentation. Higher resolution SMA observations also per- 1000 au region is 99◦. Our results suggest that the hourglass formed at 850 µm have revealed that HH211-mm hosts two 00 configuration of the field lines observed with ALMA by Cox sources separated by 0.3 (Lee et al. 2009). The first, SMM1 et al. (2018) already starts to be resolved at SMA scales. is the protostar from which the collimated outflow originates, and SMM2, in its southwest, is responsible for the southwestern BHR7-MMS extension we observe in our analysis. Modeling the jet wiggle, Lee et al. (2010) also suggested that the HH211-SMM1 source Continuum morphology at 850 µm. The SMA 850 µm con- itself might be a proto-binary source with a separation of ∼5 tinuum emission is elongated in the north-south direction. By au. Using ALMA data, Lee et al. (2019) have however recently comparison, the SMA 1.3 mm continuum emission presented questioned the nature of SMM2 as a secondary source. The com- in Tobin et al. (2018) is much more compact and marginally ex- panion source is not detected either as part of the VANDAM tended in the east-west direction, but was observed with the Very Perseus survey (Tobin et al. 2016). Extended Configuration, which has a resolution that is three to four times higher than that of the current analysis. Magnetic field orientation. The central field lines traced by the SMA observations have a north-south direction, that is, Fragmentation. BHR7-MMS is an isolated dark cloud. The they are roughly perpendicular to the outflow direction. This source does not seem to be fragmented at the intermediate average 175◦ orientation is consistent with the results from the scales probed with the SMA (Tobin et al. 2018, and this work). TADPOL survey from Hull et al. (2014) and the SCUBA-POL Recently taken but not yet published ALMA observations of the results from Matthews et al. (2009). This is also consistent source should reveal the inner morphology of the source in the with the central, northeast, and northwest field lines traced at a coming years. 0.600 resolution with the SMA by Lee et al. (2014) down to the Magnetic field orientation. To our knowledge, this is the first ALMA scales presented in Lee et al. (2018). Farther away from time that polarized dust emission is used to probe the magnetic the center, the B-field lines seem to realign in the direction of field direction in this source. We observe that B is oriented the outflow axis (see the eastern and western vectors). east-west, perpendicular to the direction of the outflow. The northern and southern vectors are slighted tilted compared to HH212

15 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Continuum morphology at 850 µm. The SMA observation re- Fragmentation. Maury et al. (2011) found that SerpS-MM18 veals a disk-like shape in the direction perpendicular to the is separated into two sources: MM18a is the primary protostar, outflow, consistent with the continuum emission detected in followed by a weaker secondary source MM18b 1000 in its south- Wiseman et al. (2001) and observed at 0.9 mm with ALMA west. This result has been confirmed by the observations of the (Codella et al. 2014). Serpens South complex by Plunkett et al. (2018). Fragmentation. SMA observations at higher resolution than Magnetic field orientation. H- and Ks-band polarization those presented in this paper have suggested that one, if not measurements have shown that the large-scale magnetic field is several, faint sources are located around the main body of globally well ordered perpendicular to the main Serpens South the HH212-mms source (Lee et al. 2008; Chen et al. 2013). filament, thus in an east-west direction (Sugitani et al. 2011). However, more recent ALMA observations by Codella et al. When we zoom in on SSMM18, the magnetic field lines are (2014) taken at a similar resolution (000. 5 resolution) did neither also oriented in this EW direction, with lines perpendicular to resolve nor detect these sources. These fainter sources detected the outflow axis. The divergence of the eastern vectors could be with the SMA are probably detections within HH212 flattened a signature of an hourglass morphology. envelope. The VANDAM team, using VLA observations, de- rived a Toomre Q parameter for this source that is consistent with a marginally unstable disk, but did not detect multiplicity in the source (Tobin et al. 2020). We therefore consider the source Appendix B: Effect of the pixel size on the mean as a single source until further analysis confirms or refutes the B-field orientation presence of additional dust peaks. Magnetic field orientation. The field lines in the central plane are oriented in a northeast-southwest direction, close to the Table B.1. Effect of the pixel size on the mean B-field orienta- outflow axis of the source. The southern vectors seem to be tion following the outflow cavity walls. We note that B traced with ALMA, in contrast, is perpendicular to the outflow direction Name B P.A. (Lee et al. 2018). The authors suggested that this orientation mean might be due to dust polarization arising from self-scattering at these small scales. 0.600 0.700 0.800 0.900 1.000

L483 Per B1-bS 26◦ 21◦ 26◦ 21◦ 22◦ Continuum morphology at 850 µm. Our SMA observations re- Per B1c 99◦ 95◦ 99◦ 97◦ 92◦ veal a dust continuum elongated in the direction perpendicular to BHR7-MMS 87◦ 90◦ 93◦ 91◦ 92◦ the outflow direction. The southwestern extension is consistent HH25-MMS 74◦ 83◦ 85◦ 86◦ - with the extension observed by Park et al. (2000) at 3.4 mm. HH211-mm 174◦ 167◦ 175◦ 162◦ 170◦ HH212 51◦ 59◦ 56◦ 57◦ 47◦ Fragmentation. L483 appears to be an isolated dense core down ◦ ◦ ◦ ◦ ◦ to the 200 × 100. 5 scales traced by the SMA observations, as has L483 8 4 23 17 16 Serp SMM18 84◦ 83◦ 84◦ 85◦ 83◦ been suggested by Jørgensen (2004) and Chen et al. (2013). Recent 1.2mm ALMA observation resolves the southwestern ex- tension, with a separate continuum source detected at a 3σ level (Oya et al. 2017). Its nature was not discussed, however. Magnetic field orientation. Polarized emission is not detected toward the center of the source, but is dectected in the south- Appendix C: Complementary tests on the mean western extension (two consistent detections). Its direction is B-field orientation estimates perpendicular to the southeast-northwest outflow direction of Other methods were developed to calculate mean polarization the source and also perpendicular to the mean B-field orientation angles, in particular, to analyze single-dish observations of dust at core scales (93◦) traced at 350 µm using SHARP by Chapman polarized emission. We provide here the B-field position angle et al. (2013). We also have a detection in the eastern part of obtained from three other averaging methods. Table C.1 gathers the source, although it is associated with weaker continuum the various estimates derived. emission (hence its high associated polarization fraction), with a ◦ B position angle of 90 . We did not take this vector into account Column (1) provides the (arithmetic, not weighted) mean B- in our calculation of the magnetic field orientation because of its field orientation within the central 1000 au region. Column (2) discrepancy with the other two detections. If the three vectors provides the B-field orientation estimated using the technique were into account, the weighted mean B position angle would 0 ◦ ◦ described in Li et al. (2006). First, we computed Q = Q/Pi and be 50 , leading to a misalignment of 55 between the magnetic U0 = U/P for each pixel in which the polarization is detected in field and the outflow orientation. This would place L483 in the i the central 1000 au region, then averaged all values of Q0 and center of the correlation observed in Fig. 3 and reinforce the U0. We then derived the position angle average using Q0,U0 and general correlation we observe. Eq. 4. Finally, Column (3) provides the B-field position angle obtained when all the Q and U fluxes of each pixel in which the Serpens South MM18 polarization is detected in the central 1000 au region are summed Continuum morphology at 850 µm. The SMA continuum emis- separately, and the position angle average was then derived from sion is extended in the western and southern part of the source. the two sums. These methods, although adapted to compute a This extension is consistent with that found from the PdBI by mean B orientation in single-dish observations with many inde- Maury et al. (2019). pendent detections with high S/N over a wide range of physical

16 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars local conditions, may not be well adapted to interferometric data that contain only a few detections with large variations in their associated errors and that emanate from rather homogeneous lo- cal conditions and large variations in their associated errors. The reference values we used in this analysis are reported in Table 4. The values of the B position angles estimated with the different averaging methods are extremely consistent with each other (with a standard deviation of 5◦ between the test and the nominal values), which is expected because the area over which the calculation was performed is small. These tests show that the main component of B in the protostellar envelopes we discussed here are, considering the intrinsic limitation of the data in hands, robust envelope-scale values, and our handling of the polarization data is therefore meaningful.

Table C.1. Results from alternative methods for the B-field po- sition angles

Name Bmean P.A.

Mean Li et al. (2006) From ΣU/ΣQ (1) (2) (3)

Per B1-bS 26.1◦ 23.6◦ 25.9◦ Per B1c 99.6◦ 92.0◦ 90.3◦ B335 54.7◦ 55.0◦ 54.7◦ BHR7-MMS 84.0◦ 84.8◦ 86.4◦ CB230 84.7◦ 85.7◦ 84.6◦ HH25-MMS 77.4◦ 78.8◦ 75.6◦ HH211-mm 173.3◦ 173.9◦ 173.4◦ HH212 51.1◦ 59.8◦ 56.6◦ HH797 110.4◦ 110.5◦ 110.4◦ IRAS03282 42.2◦ 44.7◦ 42.4◦ IRAS16293-A 139.3◦ 174.0◦ 173.3◦ L1157 149.4◦ 148.2◦ 149.0◦ L1448C 95.0◦ 94.9◦ 95.0◦ L1448N-B 22.8◦ 23.1◦ 22.8◦ L483-mm 7.9◦ 7.3◦ 7.9◦ NGC 1333 IRAS4A 53.4◦ 57.3◦ 54.0◦ NGC 1333 IRAS4B 46.9◦ 48.9◦ 49.4◦ SSMM18 84.7◦ 79.9◦ 84.0◦ SVS13-B 20.0◦ 20.8◦ 19.1◦

17 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Appendix D: Polarization intensity and fraction maps

18 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

B1-b B1-c BHR7-MMS

HH25-MMS HH211-mm HH212

Fig. D.1. For each source, the first row shows the polarization intensity maps of the sample derived from the Stokes Q and U maps obtained with the SMA at 850 µm The color scale is in Jy/beam. The Stokes I contours at -3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 σ are overlaid in blue. The filled ellipses in the lower left corner indicate the synthesized beam of the SMA maps. Their sizes are reported in Table 3. Second row: Polarization fraction map.

19 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

L483 SSMM18

Fig. D.1. continued.

20 M. Galametz et al: Polarized-dust emission in solar-type Class 0 protostars

Appendix E: Velocity maps

+ + B1-b (N2D ) B1-c (N2H ) 6.6 1.50

6.5 31°07'30" 1.55 31°09'36"

6.4 1.60

27" 33" 6.3 1.65 Galactic Latitude

6.2 Galactic Latitude 30" 24" 1.70

6.1 1.75 27"

21" 6.0 1.80 3h33m21.8s 21.6s 21.4s 21.2s 21.0s 3h33m18.4s 18.2s 18.0s 17.8s 17.6s 17.4s Galactic Longitude Galactic Longitude

+ + BHR7-MMS (N2D ) SSMM18 (N2H ) 9.0

5.0 8.8

-34°30'55" 4.8 -2°03'00" 8.6

4.6 31'00" 8.4

4.4 03" 8.2 05" 4.2 Galactic Latitude 8.0 Galactic Latitude

4.0 10" 7.8 06" 3.8 7.6 15"

3.6 h m s 8h14m24.0s 23.5s 23.0s 22.5s 18 30 04.4 04.2s 04.0s 03.8s Galactic Longitude Galactic Longitude

+ Fig. E.1. Velocity maps derived from N2H for B1-c and + SSMM18, N2D for B1-b and BHR7. Data are presented in Huang & Hirano (2013), Matthews et al. (2008), and Tobin et al. (2018) for B1-b, B1-c, and BHR7, respectively. The Serpens South MM18 data come from the PdBI CALYPSO survey.

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